P-adic-absolute-value Definition


(number theory, field theory) A norm for the rational numbers, with some prime number p as parameter, such that any rational number of the form — where a, b, and p are coprime and a, b, and k are integers — is mapped to the rational number , and 0 is mapped to 0. (Note: any rational number, except 0, can be reduced to such a form.)

According to Ostrowski's theorem, only three kinds of norms are possible for the set of real numbers: the trivial absolute value, the real absolute value, and the p-adic absolute value.WP.